login
A370264
Lexicographically earliest sequence such that each subsequence enclosed by a pair of equal values, including the endpoints, has a unique sum.
2
1, 1, 2, 1, 3, 2, 1, 3, 3, 4, 2, 1, 3, 5, 4, 2, 6, 7, 1, 3, 5, 4, 7, 6, 2, 8, 1, 5, 6, 9, 9, 3, 1, 10, 2, 8, 4, 1, 10, 6, 9, 3, 2, 5, 11, 12, 4, 3, 10, 7, 8, 2, 13, 11, 12, 4, 13, 1, 14, 3, 9, 15, 5, 6, 7, 14, 16, 6, 2, 4, 8, 12, 3, 9, 10, 11, 5, 7, 13, 1, 14
OFFSET
1,3
COMMENTS
Note that we are considering the sums of the terms between every pair of equal values, not just those that appear consecutively.
LINKS
EXAMPLE
a(2)=1 creates the pair [a(1), a(2)] = [1, 1], which gives the unique sum of 2.
a(4)=1 creates two unique sums: [1,2,1] = sum of 4 and [1,1,2,1] = sum of 5.
a(8)=3 creates one unique sum: [3,2,1,3] = sum of 9.
PROG
(Python)
from itertools import islice
def agen(): # generator of terms
s, a = set(), []
while True:
an, allnew = 0, False
while not allnew:
allnew, an, sn = True, an+1, set()
for i in range(len(a)):
if an == a[i]:
t = sum(a[i+1:]) + 2*an
if t in s or t in sn: allnew = False; break
sn.add(t)
yield an; a.append(an); s |= sn
print(list(islice(agen(), 81))) # Michael S. Branicky, Feb 14 2024
CROSSREFS
Cf. A370264 (excluding endpoints), A366493, A366624, A366631, A366625.
Sequence in context: A115624 A076291 A275015 * A211189 A194968 A194980
KEYWORD
nonn
AUTHOR
Neal Gersh Tolunsky, Feb 13 2024
EXTENSIONS
a(16) and beyond from Michael S. Branicky, Feb 14 2024
STATUS
approved